Question

Please solve with explanation

Answer 1

Answer:

large area: small area = 100:25 = 4:1

Step-by-step explanation:

Mid-Segment of a triangle is always parallel to the third side, and the length of the midsegment is half the length of the third side.

(x₁,y₁) (x₂,y₂) (x₃,y₃): A(-10,30), B(30,50, C(-40,20)

XY = 1/2 AC , YZ = 1/2 AB , ZX = 1/2 BC

X (10,40) , Y (-5,35) , Z (-25,25) : X(x'₁,y'₁), Y(x'₂,y'₂), Z(x'₃,y'₃)

area of triangle by 3 vertices: (x₁,y₁) (x₂,y₂) (x₃,y₃) is

a = abs[x₁(y₂-y₃)+x₂(y₃-y₁)+x₃(y₁-y₂)] / 2  ... this is just a common formula for any triangle

a = abs(-10*30 + 30*-10 + -40*-20) / 2 = 100

a' = abs(10*10 + -5*-15 + -25*5) / 2 = 25

a/a' = 100/25 = 4/1